Standard #: MA.5.FR.2.4

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.2.2
• MA.5.AR.1.3

 

Terms from the K-12 Glossary

• NA

 

Vertical Alignment

Previous Benchmarks

• MA.4.FR.2.4

 

Next Benchmarks

• MA.6.NSO.2.2
• MA.6.NSO.2.3

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to experience division with whole number divisors and unit fraction dividends (fractions with a numerator of 1) and with unit fraction divisors and whole number dividends. This work prepares for division of fractions in grade 6 (MA.6.NSO.2.2) in the same way that in grade 4 (MA.4.FR.2.4) students were prepared for multiplication of fractions. 

• Instruction should include the use of manipulatives, area models, number lines, and emphasizing the properties of operations (e.g., through fact families) for students to see the relationship between multiplication and division (MTR.2.1).
• Throughout instruction, students should have practice with both types of division: a unit fraction that is divided by a non-zero whole number and a whole number that is divided by a unit fraction. 
• Students should be exposed to all situation types for division (refer to Situations Involving Operations with Numbers (Appendix A). 
• The expectation of this benchmark is not for students to use an algorithm (e.g., multiplicative inverse) to divide by a fraction. 
• Instruction includes students using equivalent fractions to simplify answers; however, putting answers in simplest form is not a priority.

 

Common Misconceptions or Errors

• Students may believe that division always results in a smaller number, which is true when dividing a fraction by a whole number, but not when dividing a whole number by a fraction. Using models will help students develop the understanding needed for computation with fractions.

 

Strategies to Support Tiered Instruction

• Instruction includes making the connection to models and tools previously used to understand division as equal groups or sharing. The teacher uses models to develop the understanding needed for computation with fractions.
• For example, 8 ÷ $\frac{\text{1}}{\text{4}}$ can be shown using a model of 8 wholes divided into parts of size $\frac{\text{1}}{\text{4}}$. The quotient would be the total number of $\frac{\text{1}}{\text{4}}$ pieces. The model below would show that 8 ÷ $\frac{\text{1}}{\text{4}}$ = 32. 

• For example, $\frac{\text{1}}{\text{4}}$ divided into $\frac{\text{1}}{\text{4}}$ ÷ 8 can be represented using the below model. One-fourth is divided into 8 equal parts, each part is $\frac{\text{1}}{\text{32}}$ of the whole.

• Instruction includes real-world situations to interact with the content. The teacher provides students with a division expression with a real-world context and provides items to represent the situation to allow connections to be made. 
  • For example, the teacher provides students with the following situation: “The teacher brought in 8 brownies to split between the class. She cut the brownies into pieces of size $\frac{\text{1}}{\text{4}}$ so there would be enough for the whole class. How many $\frac{\text{1}}{\text{4}}$ pieces will there be?" The teacher provides students with images of eight brownies (or models to represent them) and has them divide or cut them into $\frac{\text{1}}{\text{4}}$ pieces to determine how many pieces they will have (32 pieces). 
  • For example, the teacher provides students with the following situation: “The teacher baked a pan of brownies. All but $\frac{\text{1}}{\text{4}}$ of the pan was eaten. She brought in the remaining $\frac{\text{1}}{\text{4}}$ and divided it into 8 equal pieces for her co-teachers. What 4 fraction of the whole pan will each person get?” The teacher provides students with an image of a pan of brownies with $\frac{\text{1}}{\text{4}}$ left (or model to represent it). The students divide the $\frac{\text{1}}{\text{4}}$ portion into 8 equal pieces. The teacher then connects the 4 remaining part of the brownies to the whole pan so that students can make the connection to the total number of the smaller pieces representing $\frac{\text{1}}{\text{32}}$ of the whole. 

 

Instructional Tasks

Instructional Task 1 (MTR.5.1, MTR.7.1) 

Part A. Emily has 2 feet of ribbon to make friendship bracelets. Use models and equations to answer the questions below. 

• a. How many friendship bracelets can she make if each bracelet uses 2 feet of ribbon? 
• b. How many friendship bracelets can she make if each bracelet uses 1 foot of ribbon? 
• c. How many friendship bracelets can she make if each bracelet uses 1 half foot of ribbon? 
• d. How many friendship bracelets can she make if each bracelet uses 1 third foot of ribbon? 
• e. How many friendship bracelets can she make if each bracelet uses 1 fifth foot of ribbon? 

Part B. Do you see any patterns in the models and equations you have written? Explain.

 

Instructional Items

Instructional Item 1 

• What is the quotient of $\frac{\text{1}}{\text{3}}$ ÷ 5?
•  a. $\frac{\text{1}}{\text{15}}$ 
• b. 15 
• c. $\frac{\text{5}}{\text{3}}$  
• d. $\frac{\text{3}}{\text{5}}$  

 

Instructional Item 2 

How many fourths are in 8 wholes? 

• a. 4 
• b. 8 
• c. 16 
• d. 32 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.